Where were you between the hours of 1pm and 3pm on 23 May 2004?

If you were in Monaco, consider yourself a suspect - or at least a witness - in Formula 1's biggest unsolved mystery.

A $300,000 diamond was last seen stuck to the front of an F1 car before it crashed on the first lap of the Grand Prix and it still has not been found 22 years later.

Did someone pick it up? Was it swept up with all the debris? Did it slip down a drain? Was it even a real diamond?

Someone, somewhere, knows something.

The reason why a 1.4 carat diamond was attached to the most delicate part of a car that reaches 200mph in a race was straightforward: publicity.

Jaguar Racing's results on the track had been mediocre at best since becoming an F1 team in 2000 and by 2004 its parent company Ford had decided it would be pulling them out of the sport.

"My job flipped from primarily running the team to primarily selling the team and finding a new owner or they would shut it down," former team principal Tony Purnell tells BBC Sport.

"It was probably the worst year of my life. Particularly because for the first few months I was sworn to secrecy."

His team needed some good PR to divert attention away from performance and improve its appeal.

They had enjoyed a successful promotional weekend in Silverstone the previous season thanks to a tie-up with Terminator 3 and so director of communications Nav Sidhu was looking to recreate the magic with another bit of help from a movie.

"I'd heard on the grapevine, around about the winter of 2003, that they were making Ocean's Twelve and we discovered that they were shooting some of the scenes in Monte Carlo," Sidhu says.

"One thing led to another and before you knew it, we had agreed [a deal] with George Clooney, Brad Pitt and Matt Damon."

Sidhu had arranged with legendary Hollywood producer Jerry Weintraub to have the film's branding and stars take over the team for the Monaco weekend.

The film plot centred on an audacious theft of a diamond-encrusted Faberge egg. Sidhu decided he wanted some sparkle on his cars too at the most glamorous race in the F1 calendar.

Sidhu negotiated with diamond company Steinmetz that the two Jaguar cars would have gems - which would today be worth about $1m in total - attached to them.

What happened next, though, was not part of the script.

While the champagne corks were popping on nearby mega yachts in the principality, the diamonds were being hand-delivered into the garages. There were two that would be mounted on to the car and a larger gem just for the photos.

The diamonds for the cars were encased by steel and fixed to the nose cones. One on experienced driver Mark Webber's car and one on rookie Christian Klien's.

Webber was starting from 11th place in the grid and Klien - in only his sixth race - was starting from 14th. They weren't expected to challenge for the podium, but they were expected to bring the diamonds back.

Monaco's street circuit is demanding, with narrow roads, tight turns and a tunnel.

Overtaking is difficult and crashes are common - as Klien soon found out.

In a chaotic first lap, the Austrian made contact with one of the Jordan cars exiting the Mirabeau corner. This damaged the front of his car - where the diamond was - and led to a slow collision with the barriers at the famous Loews hairpin.

Klien climbed out unhurt but the front of the car was crumpled.

It was not long before Sidhu had the diamond company on the phone asking if they would get their diamond back.

"I can't remember what I answered, but it certainly wasn't 'yes'," he says.

He couldn't even get on to the track to have a look as the race had another 76 laps to go and only then would the car - which had been lifted off the track by a crane and left behind the barriers - return to the garage.

"I was consumed with getting to that spot as quickly as I possibly could," Sidhu says.

"That hour and a half waiting for the race to finish felt like a day and a half, every single lap was just like pulling teeth."

By the time he had the chance to have a look, there was no sign of the diamond.

But there were plenty of theories.

Theory: it was not a real diamond

Sidhu completely denies the rumours of a fake diamond.

"I've learned that any diamond company is not going to go out there, particularly in the public domain, and use fake diamonds because clearly there's a high risk of being caught," he says.

"Had we used a fake diamond in that car and what took place took place, then clearly the embarrassment and the disrepute it would bring Jaguar, and Formula 1 for that matter, was too high risk.

"There's been loads of conspiracy theories about was it a real diamond or was Christian told to crash his car and I think that's what's given the story its life - there's a mystery to this story and that mystery will always breed different theories."

Purnell backs up the legitimacy of the diamond, recalling a conversation he had with the managing director of the team, David Pitchforth.

"David said, 'Tony, it was definitely real because when they came to the office with it, I picked the diamond up, went to the window and scratched the window' because that's how to tell.

"Hearing that from Dave, I'm in no doubt it was the real thing that was put on the car.

"I don't know if one of our mechanics was switched on enough to make a fake, but I don't think so."

Theory: someone pocketed it

"I think somebody probably just picked it up, put it in their pocket and... they're probably smiling and thinking, 'it's in my drawer'," says Purnell.

"I do think also that a fairly large diamond zooming through at 100 miles an hour probably shattered. Somebody's got a little bit, somebody else has got another [little bit].

"Maybe, sadly, just some guy was sweeping up the road or one of those trucks with the brushes and it all went down the sewer.

"It did occur to me that the ultimate thing would be if Clooney, Pitt and Damon had contrived to steal it because it was so in line with Ocean's Eleven. But that was a fantasy too far."

There would have been hundreds, if not thousands, of people in the area because within an hour or so of the end of the race the circuit would have been returned to public roads.

Sidhu is pretty certain about what happened to the diamond: "Someone's picked it up.

"What people tend to do is, believe it or not, pick up bits of tyre rubber, you know, claim that as Michael Schumacher's front tyre rubber or whatever they can find.

"Somebody may have picked it up not having any idea it came off a car.

"There's a lot of diamonds in Monte Carlo. There's a lot of people walking around Monte Carlo with a lot of jewellery and a lot of stones.

"Somebody dropped a diamond in Monte Carlo. Well, they're not going to miss that, are they? Probably not."

Theory: Klien crashed on purpose

Sidhu says the cost of the damage to the car was more than the cost of the diamond, which reports at the time said was uninsured.

And points and a good result in the race were more valuable to the team and individuals than a diamond or the publicity a crash would bring. It was simply not worth crashing on purpose.

"For us, bringing two cars home, ideally in the points, had far bigger commercial benefits to us in terms of constructors' points, broadcast money, and more importantly, trying to retain our sponsors and trying to protect the integrity of the team," Sidhu explains.

Klien drove straight into the barriers right in front of the marshals so would not have had the chance to start looking for a diamond or picking it up even if he had wanted to.

"Christian didn't try and say all the brakes failed or anything like that, he's just said 'I made a rookie mistake'," says Purnell.

"He was a young guy, first time, made a mistake, it happens. Doesn't usually happen with a $300,000 diamond flying into the crowd or wherever it went, but I'm sure Christian wasn't really aware of the diamond.

"No amount of money would have got Christian to do that [crash on purpose]. He wanted to make a success of what he was doing."